Taking dance lessons but I need to protect my shoes

Break them in. Use them for what you need them for.

I would just find a different pair of heels the same height and practice in those.

This is practice.. imagine the wedding?

I say return them and get something you won't feel bad about damaging

For your heels, they have heel protectors. Ask your teacher about it. I would highly recommend practicing a few time with those shoes so you know you can dance in them.

Another option is to get nice ballroom dance shoes (suede bottom). They are pretty and very comfortable. You can do a quick change right before the dance.

ETA: do not use sock or medical shoes covers! You will slip and fall!

I agree, you need to practice dancing in them as the steps are different in different shoes ... I learned that even though mine have a back strap, my feet can still slip out of them during the dance if I'm not careful. Plus you need to break them in anyway.

They have slip resistant sole protectors on amazon!

If you want to practice in the shoes, heel protectors can protect the heel (check the shape and size of your heel before you order to make sure you get a good fit), and leg warmers to protect the main part of the shoes. You can either cut a hole in them to poke your heel through to keep them pulled down, or just scrunch them down low. You want to make sure the leg warmers are tight enough that they grip your shoes so they don't slip down and make you slide.

ETA, you could also wear other shoes (heels or not) for the majority of your sessions and then switch into your wedding shoes for the last practice or two. Minimizes wear on your wedding shoes but still gives you the opportunity to practice in them before the big day.

Get another pair of shoes to dance in- when you actually KNOW what you're dancing- and now you're just rehearsing and not learning- start wearing the new shoes- about 2 weeks about.

Or go buy real dance shoes and just use those all night.